Find the values of m such that the line does not touch the parabola

[brinethery]

Homework Statement

for what values of m does the line with equation y = mx - 12 not intersect or touch the parabola with equation y = 2x^2-x-10. Please show working out & explain.

Homework Equations

The Attempt at a Solution

This question was asked on openstudy and there hasn't been an answer to it yet. It's been 5 years since I've taking algebra and pre-calc, so there's certain things I don't remember how to do such as this question.

Would anyone know how to approach this? I'm just extremely curious :-)

 

[HallsofIvy]

At a point, (x,y), where the two graphs intersect, the x and y values must be the same- that is, there exist a value of x such that $y= 2x^2- x- 10= mx- 12$. That's a quadratic equation, it reduces to $2x^2- (1-m)x+ 2= 0$, and so has either 2 real roots (the line crosses the parabola), 1 double root (the line is tangent to the parabola), of no real roots (the line does not touch the parabola). Use the quadratic formula to determine what m must be so that equation has no real roots.